Solve the Problem $\mathrm { A } = \left[ \begin{array} { r r r } 1 & - 3 & 0 \\ - 4 & 0 & 2 \\ 4 & 1 & - 2 \end{array} \right]$

question 75

Multiple Choice

Solve the problem.
-Let $\mathrm { A } = \left[ \begin{array} { r r r } 1 & - 3 & 0 \\ - 4 & 0 & 2 \\ 4 & 1 & - 2 \end{array} \right]$ and $\mathbf { b } = \left[ \begin{array} { r } 9 \\ - 6 \\ 4 \end{array} \right]$ .
Define a transformation $\mathrm { T }$ : $\mathfrak { R } ^ { 3 } \rightarrow \mathbb { R } ^ { 3 }$ by $\mathrm { T } ( \mathbf { x } ) = \mathrm { Ax }$ .
If possible, find a vector $x$ whose image under $\mathrm { T }$ is $\mathbf { b }$ . Otherwise, state that $\mathbf { b }$ is not in the range of the transformation $\mathrm { T }$ .

• A)
• \[\left[ \begin{array} { r }
• 3 \\
• - 2 \\
• 0
• \end{array} \right]\]
• B) \(\mathbf { b }\) is not in the range of the transformation \(T\).
• C) \(\left[ \begin{array} { r } 3 \\ 3 \\ - 2 \end{array} \right]\)
• D)
• \[\left[ \begin{array} { r }
• 3 \\
• - 2 \\
• 3
• \end{array} \right]\]

Know how to properly format fields to accurately display the stored data.

Understand the significance and application of field size and decimal places in data representation.

Explain the process and reasoning behind setting up field properties for special requirements (e.g., fields that must contain values, unique constraints).

Recognize the importance of matching data types and field properties to the nature of the data being stored.